Since 1986 the Mathematics section at ICTP has played an important role in fostering mathematics research and education in developing countries. Research is carried out in various fields of Mathematics by the permanent staff, postdocs, and graduate students, as well as by scientific visitors from all over the world.

Typically, the section organizes from 5 to 10 focused activities a year involving an average of 100 participants. These activities are the core of the section's activities and are crucial for disseminating current mathematics knowledge of the highest level as widely as possible.

In addition the Mathematics section, like all the other sections at ICTP, participates in the Diploma program. Since 2011 Diploma students can apply to stay on to work on a PhD in Mathematics in a joint program with SISSA.

Europe/Rome2020-06-23 16:00:002020-06-23 17:00:00Basic notions seminar on mean curvature flow of closed hypersurfaces
Information on how to register will follow soon.
Abstract: The seminar will start with the definition of what is mean curvature flow of a closed hypersurface, illustrated with some basic examples. Next, I will recall the variational nature of the flow and some of the main well-known results, such as Grayson theorem for the evolution of plane curves, and Huisken convexity preserving theorem. At the end of the seminar, some more advanced topics will be mentioned.
Zoom MeetingICTPpio@ictp.it
23 Jun 2020

Europe/Rome2020-06-24 17:00:002020-06-24 18:00:00Ergodic and thermodynamic properties of pseudo-Anosov diffeomorphisms
Abstract: We discuss the thermodynamic and ergodic properties of a smooth realization of pseudo-Anosov surface homeomorphisms. In this realization, pseudo-Anosov map is uniformly hyperbolic outside of a neighborhood of a set of singularities, and the trajectories are slowed down so the differential is the identity at the singularities. Using Young towers, we prove existence and uniqueness of equilibrium measures for geometric $t$-potentials. This family of equilibrium measures includes a unique smooth SRB measure and a measure of maximal entropy, the latter of which has exponential decay of correlations and the Central Limit Theorem.
Zoom MeetingICTPpio@ictp.it
24 Jun 2020

Europe/Rome2020-07-02 14:00:002020-07-02 15:00:00Math Associates Seminar: Closed Geodesics on Surfaces without Conjugate Points
Abstract: We obtain Margulis-type asymptotic estimates for the number of free homotopy classes of closed geodesics on certain manifolds without conjugate points. Our results cover all compact surfaces of genus at least 2 without conjugate points. This is based on a join work with Vaughn Climenhaga and Gerhard Knieper.
Zoom MeetingICTPpio@ictp.it
2 Jul 2020

Europe/Rome2020-06-29 08:00:002020-07-03 22:00:00Complex Analysis, Geometry and Dynamics ECM-ICTP 2020 * CANCELLED * | (smr 3457)Note: ICTP has suspended all educational activities from 24 February up to 26 June as precautionary measures due to COVID-19; more details at
https://www.ictp.it/about-ictp/media-centre/news/2020/2/ictp_suspend_activities.aspx
The goal is to bring together leading researchers worldwide in complex analysis, geometry, and dynamics, with the aim of enhanced future collaboration. These fields are strongly interrelated, and in order to be able to solve deep challenging problems it is becoming necessary to pursue synergies among them to a bigger degree than in the past.
Topics:
Holomorphic approximation theory
L2 techniques, plurisubharmonic functions, complex pluripotential theory
Complex dynamics in higher dimensions
Holomorphic directed systems, contact systems
Applications of complex analysis to minimal surfaces
Flexibility versus rigidity in complex geometry
Cauchy-Riemann geometry
Monge-Ampėre equations and Kähler manifolds
There have been major recent advances in all these topics which the speakers will report on. It is becoming increasingly evident that a deeper level of cooperation will be needed for further progress.
Speakers:
A. ALARCÓN, University of Granada, Spain
D. ANGELLA, University of Firenze, Italy
F. BRACCI, University of Rome II-Tor Vergata, Italy
F. DENG, University of Chinese Academy of Sciences, China
B. DRINOVEC DRNOVŠEK, University of Ljubljana, Slovenia
P. EBENFELT, University of California-San Diego, USA
V. GUEDJ, University of Toulouse, France
J.-M. HWANG, Korea Institute for Advanced Study, Korea
S. KOLODZIEJ, University of Cracow, Poland
F. KUTZSCHEBAUCH, University of Berne, Switzerland
B. LAMEL, University of Vienna, Austria
F. LÁRUSSON, University of Adelaide, Australia
X. MING, University of California-San Diego, USA
S. NEMIROVSKI, Steklov Mathematical Institute, Russia
T. OHSAWA, Nagoya University, Japan
H. PETERS, University of Amsterdam, The Netherlands
D. PHONG, Columbia University, USA
N. SHCHERBINA, University of Wuppertal, Germany
B. STENSØNES, NTNU, Norway
L. STUDER, Universidad Complutense de Madrid, Spain
J. WINKELMANN, Bochum University, Germany
E. F. WOLD, University of Oslo, Norway
E. WULCAN, University of Gothenburg, Sweden
A. ZIMMER, Louisiana State University, USA
Grants:
A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is no registration fee.
ICTPICTPpio@ictp.it
29 Jun 2020
- 3 Jul 2020

Europe/Rome2020-07-21 08:00:002020-07-31 22:00:00International Conference on Representations of Algebras, ICRA 2020 Workshop and Conference * CANCELLED * | (smr 3463)Note: ICTP has suspended all educational activities from 24 February up to 26 June as precautionary measures due to COVID-19; more details at
https://www.ictp.it/about-ictp/media-centre/news/2020/2/ictp_suspend_activities.aspx
ICRA is a biannual international conference series started in 1974. It brings together well-established experts and young researchers in representation theory and in allied fields where representation theory is applied.
The first week will consist of a workshop with six lecture series, including introductory talks and on topics of particular current interest, such as recent links to both topological data analysis and to mathematical physics. One of the lecture series will be devoted to the mathematical heritage of Ragnar Buchweitz.
The second week will be a conference with invited speakers in addition to contributed talks, both in plenary and in parallel sessions.
Topics:
Representation theory of algebras and its applications, including:
-Topological Data Analysis
-Cluster algebras
-Non-commutative algebraic geometry
-Modular representation theory.
Workshop Speakers :
M. BOTNAN, Amsterdam
P. ETINGOF, MIT
S. FOMIN, Michigan
S. IYENGAR, Utah
B. KELLER, Paris 7
S. SCHROLL, Leicester
Conference Speakers:
P. BALMER, UCLA
A. BARBIERI, Sheffield
M. CAORSI, former SISSA
T. HAUSEL, IST Austria
L. WILLIAMS, Harvard
S. WITHERSPOON, Texas
Scientific Committee:
J. ASADOLLAHI, Isfahan
C. GEISS, Mexico City
O. IYAMA, Nagoya
B. KELLER, Paris
S. OPPERMANN, NTNU
J. PEVTSOVA, Washington
R. SCHIFFLER, Connecticut
S. SCHROLL, Leicester
J. TRLIFAJ, Prague
M. VAN DEN BERGH, Hasselt
Grants:
A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is a registration fee, but this is waived for supported participants from developing countries.
For further information regarding the International Conference on Representations of Algebras, ICRA 2020 Workshop and Conference please visit the following link:
https://wiki.math.ntnu.no/icra2020/start
Applications for both the Workshop and the Conference can be submitted at the following link: http://indico.ictp.it/event/9108/ by clicking 'Apply here'
Applications for the Conference ONLY can be submitted at the following link:
http://indico.ictp.it/event/9181/ by clicking 'Apply here'
ICTPICTPpio@ictp.it
21 Jul 2020
- 31 Jul 2020

Europe/Rome2020-07-27 08:00:002020-07-31 22:00:00International Conference on Representations of Algebras, ICRA 2020 Conference * CANCELLED * | (smr 3502)Note: ICTP has suspended all educational activities from 24 February up to 26 June as precautionary measures due to COVID-19; more details at
https://www.ictp.it/about-ictp/media-centre/news/2020/2/ictp_suspend_activities.aspx
ICRA is a biannual international conference series started in 1974. It brings together well-established experts and young researchers in representation theory and in allied fields where representation theory is applied.
The first week will consist of a workshop with six lecture series, including introductory talks and on topics of particular current interest, such as recent links to both topological data analysis and to mathematical physics. One of the lecture series will be devoted to the mathematical heritage of Ragnar Buchweitz.
The second week will be a conference with invited speakers in addition to contributed talks, both in plenary and in parallel sessions.
Topics:
Representation theory of algebras and its applications, including:
-Topological Data Analysis
-Cluster algebras
-Non-commutative algebraic geometry
-Modular representation theory.
Workshop Speakers :
M. BOTNAN, Amsterdam
P. ETINGOF, MIT
S. FOMIN, Michigan
S. IYENGAR, Utah
B. KELLER, Paris 7
S. SCHROLL, Leicester
Conference Speakers:
P. BALMER, UCLA
A. BARBIERI, Sheffield
M. CAORSI, former SISSA
T. HAUSEL, IST Austria
L. WILLIAMS, Harvard
S. WITHERSPOON, Texas
Scientific Committee:
J. ASADOLLAHI, Isfahan
C. GEISS, Mexico City
O. IYAMA, Nagoya
B. KELLER, Paris
S. OPPERMANN, NTNU
J. PEVTSOVA, Washington
R. SCHIFFLER, Connecticut
S. SCHROLL, Leicester
J. TRLIFAJ, Prague
M. VAN DEN BERGH, Hasselt
Grants:
A limited number of grants are available to support the attendance of selected participants, with priority given to participants from developing countries. There is a registration fee, but this is waived for supported participants from developing countries.
For further information regarding the International Conference on Representations of Algebras, ICRA 2020 Workshop and Conference please visit the following link:
https://wiki.math.ntnu.no/icra2020/start
Applications for both the Workshop and the Conference can be submitted at the following link: http://indico.ictp.it/event/9108/ by clicking 'Apply here'
Applications for the Conference ONLY can be submitted at the following link:
http://indico.ictp.it/event/9181/ by clicking 'Apply here'
ICTPICTPpio@ictp.it
27 Jul 2020
- 31 Jul 2020

Europe/Rome2020-08-03 08:00:002020-08-14 22:00:00EAUMP-ICTP School: Topics in Concrete Mathematics | (smr 3465). CANCELLED
DUE TO THE COVID19 PANDEMIC THIS SCHOOL HAS BEEN CANCELLED.
--------------------- Original text purpose of the School ----------------------
This School will be held at the ICTP-East African Institute for Fundamental Research [EAIFR] in Kigali, Rwanda; it will offer students concrete and effective mathematical tools from algebra, group theory and geometry that can be applied to any scientific field.
Description of Courses:
Advanced linear algebra
This goes beyond a first course on the subject. Topics like Jordan normal form will be studied as well as bilinear forms, multilinear forms and tensor products;
Groups, Counting and FFT
We start with group theory via rotations in 3d space; this will be used in Pólya counting problems. We then moves on to character theory culminating in fast Fourier transform;
Introduction to Lie Algebras
The course introduces Lie algebras and aims towards of the classification of semisimple Lie algebras which is widely considered one of the most elegant results in mathematics;
Modular forms
The course introduces modular forms. We will study many concrete examples, like the Eisenstein series, from which we will construct the finite dimensional spaces of modular forms of any weight.
Kigali - RwandaICTPpio@ictp.it
3 Aug 2020
- 14 Aug 2020

Opportunities

Every year the Mathematics Group offers research opportunities for outstanding mathematicians from developing countries, for short and long-term visits, as well as postdoctoral fellowships, through the Mathematics Research Fellowships programme. A call for postdoctoral fellowships with a starting date of September 2020 is now open. The application deadline is 5 January 2020.
Other research and education opportunities in mathematics are
available through the ICTP's Postgraduate Diploma Programme as well as
its Associateship Scheme.